ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Factoring Quadratic Trinomials

Updated on September 5, 2011

FACTORING QUADRATIC TRINOMIALS

One of the most important lessons in Algebra is factoring quadratic trinomials. In this hub I present some exercises with their solutions and techniques.


Exercise Number One : FactorX2 + 10X + 16

The factor of a quadratic trinomial are two binomials such that the first term of every binomial are the factorsof X2 and the second term of every binomial are the factors of 16.

Our factors are :(X + 8) (X + 2)

Before accepting this as a factor you have to test : Product of the outer terms plus the product of the inner terms must be equal to the middle term of the trinomial you are factoring.

Let us see:2X +8X= 10X

10X is the middle term of the trinomial therefore our factors are correct.


Exercise Number Two : FactorX2 + 3X – 28

We notice that the sign of the third term of the trinomial we are factoring is negative therefore the factors must be a positive and a negative number for opposite sign gives a negative product. We also notice that the sign of the middle term is positive therefore the product with a bigger absolute value must be positive.

Our factors are : (X + 7 ) (X – 4)

Outer product : -4X

Inner product also the product with a bigger absolute value: 7X

Let us see : 7X + -4X=3X

3X is the middle term of the trinomial therefore our factors are correct.


Exercise Number Three : Factor3X2 – 10XY – 8Y2

We notice that the sign of the middle term is negative therefore the product with a bigger absolute value must be negative.

Our factors :(3X + 2Y ) (X – 4Y)

Outer product also the product with a bigger absolute value : -12XY

Inner product : 2XY

-12XY + 2XY = -10XY

-10XY is the middle term of the trinomial therefore our factors are correct.


Exercise Number Four : Factor 4X2 -19X + 12

We notice that the sign of the third term of the trinomial we are factoring is positive while the sign of the middle term is negative. In this case the sign of both factors of the third term must be both negative to follow the rule that same sign gives positive product. They are both negative because the sign of the middle term is negative.

Our factor : (4X – 3) ( X – 4)

Outer product : (4X)(-4)= -16X

Inner product: ( X)(-3)= -3X

-16X + -3X= -19X

-19X is the middleterm of the trinomial we are factoring therefore our factors are correct.

working

This website uses cookies

As a user in the EEA, your approval is needed on a few things. To provide a better website experience, hubpages.com uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at: https://corp.maven.io/privacy-policy

Show Details
Necessary
HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
LoginThis is necessary to sign in to the HubPages Service.
Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
AkismetThis is used to detect comment spam. (Privacy Policy)
HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the googleapis.com or gstatic.com domains, for performance and efficiency reasons. (Privacy Policy)
Features
Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
MavenThis supports the Maven widget and search functionality. (Privacy Policy)
Marketing
Google AdSenseThis is an ad network. (Privacy Policy)
Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
Index ExchangeThis is an ad network. (Privacy Policy)
SovrnThis is an ad network. (Privacy Policy)
Facebook AdsThis is an ad network. (Privacy Policy)
Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
AppNexusThis is an ad network. (Privacy Policy)
OpenxThis is an ad network. (Privacy Policy)
Rubicon ProjectThis is an ad network. (Privacy Policy)
TripleLiftThis is an ad network. (Privacy Policy)
Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
Statistics
Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)
ClickscoThis is a data management platform studying reader behavior (Privacy Policy)